Causal Effects and Experiments

GVPT399F: Power, Politics, and Data

Causes and effects

Our goal is to better understand what factors lead to certain outcomes of interest.

  • Does increasing the number of voting booths close to a potential voter make that person more likely to vote?

  • Do peace treaties signed with factionalized rebel groups more often lead to a return to conflict than those signed with a single, cohesive group?

  • Does trade between two countries make war between them less likely?

Causes and effects

These are causal statements:

  • More local voting booths \(\rightarrow\) More likely to vote

  • More factionalization \(\rightarrow\) More likely to restart conflict

  • Trade \(\rightarrow\) Less likely to go to war

How to identify causes and their effects

Proving that changes to one factor cause changes to another is very tricky!

  • Need to account for all the other factors

The efficacy of international election monitors

Do international monitors cause less election-day fraud in democratic elections?

  • Number of elections monitored by international observers exploded throughout the 2000s

  • But do monitors increase the chances the election will be free and fair?

  • In other words, are they effective?

The efficacy of international election monitors

Dr Susan Hyde set out to answer this very question. From her article (page 39):

If the presence of international observers causes a reduction in election-day fraud, the effect of observers should be visible at the subnational level by comparing polling stations that were visited by observers with those that were not visited. More specifically, if international monitoring reduces electionday fraud directly, all else held equal, the cheating parties should gain less of their ill-gotten vote share in polling stations that were visited by international monitors.

Causal relationships

Refers to the directional connection between a change in one variable and a corresponding change in another.

  • The direction matters!

  • Treatment variable: the variable causing changes to another variable.

  • Outcome variable: the variable changing as a result of changes to another variable (the treatment).

Treatment and outcome variables

We want to test whether the presence of international monitors (treatment) leads to less election day fraud (outcome).

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station

Treatment variable

At any given polling station in any given election, monitors may be: 1) present, or 2) not present.

Two different conditions:

  • Treatment: condition with treatment (monitors are present)

  • Control: condition without treatment (monitors are not present)

Outcome variable

At any given polling station in any given election, fraud may: 1) occur, or 2) not occur.

Observing our outcome

Sometimes it can be hard to observe our outcome of interest.

  • How might we see all election-day fraud?

  • How might we measure it?

Observing our outcome

Hyde’s answer: vote-share!

International election monitors present at polling stations \(\rightarrow\) Less election-day fraud at that station \(\rightarrow\) Lower vote-share for the cheating party

Individual causal effects

We want to know whether the treatment causes a change in our outcome of interest.

What might this look like in the real world?

  • Imagine we are looking at a specific election

  • Five polling stations

Parallel worlds

Hypothetical election

ID Monitored vote % Non-monitored vote %
1 14.88 97.47
2 27.54 90.27
3 56.69 77.21
4 18.64 92.54
5 20.23 76.62

Individual effects

The only difference between these two conditions is the presence of international monitors!

  • The difference between vote shares under these conditions is caused by the monitors.

Individual effects

ID Monitored vote % Non-monitored vote % Difference (%)
1 14.88 97.47 -82.59
2 27.54 90.27 -62.73
3 56.69 77.21 -20.52
4 18.64 92.54 -73.90
5 20.23 76.62 -56.39

No parallel worlds

Sadly for us, we cannot create parallel worlds…

What now?

ID Monitored Monitored vote % Non-monitored vote % Difference
1 1 14.88 NA NA
2 1 27.54 NA NA
3 0 NA 77.21 NA
4 0 NA 92.54 NA
5 0 NA 76.62 NA

Average causal effects

We need to move away from looking at individuals and start to look for patterns in our group.

Back to our parallel worlds

ID Monitored vote % Non-monitored vote % Difference
1 14.88 97.47 -82.59
2 27.54 90.27 -62.73
3 56.69 77.21 -20.52
4 18.64 92.54 -73.90
5 20.23 76.62 -56.39

Difference of averages across all individuals

What was the average vote share received in each world?

Avg. monitored vote % Avg. non-monitored vote % Difference
27.6 86.82 -59.22

Back to reality

ID Monitored Monitored vote % Non-monitored vote % Difference
1 1 14.88 NA NA
2 1 27.54 NA NA
3 0 NA 77.21 NA
4 0 NA 92.54 NA
5 0 NA 76.62 NA

Difference-of-means

What was the average vote share received in each group?

Avg. monitored vote % Avg. non-monitored vote % Difference
21.21 82.12 -60.91

How on Earth does this work so well?

Randomization!

  • Monitors were assigned to polling stations randomly (for example, with the flip of a coin)

  • This created two groups of stations that were roughly identical on average to one another prior to treatment

  • This mimics what happens when we split our world into two (creating two literally identical groups)

Our goal

We want two groups that are completely identical to one another prior to treatment.

  • This allows us to compare their outcomes after treatment and claim that the treatment caused differences in those outcomes (if any differences exist)

Our goal

Next best thing

Instead, we should try to make two groups that are as similar as possible to each other prior to treatment.

The magic of randomization

Perfectly random assignment does this very well!

Don’t take my word for it

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Our group

ID Height Weight Eye colour
1 164.29 72.48 Blue
2 173.32 52.67 Brown
3 164.59 91.12 Brown
4 166.34 81.78 Grey
5 166.41 83.85 Green
6 178.75 81.98 Green
7 169.14 71.24 Brown
8 180.09 72.07 Grey
9 173.46 68.81 Brown
10 166.24 72.66 Brown
11 177.61 79.56 Blue
12 179.79 74.09 Brown
13 174.14 89.51 Brown
14 171.52 78.91 Green
15 158.24 75.43 Green
16 165.07 84.19 Grey
17 180.27 92.09 Brown
18 150.41 96.27 Brown
19 180.02 71.62 Brown
20 163.55 71.17 Blue
21 175.05 82.77 Green
22 171.54 98.17 Green
23 159.25 79.06 Grey
24 169.00 67.57 Brown
25 170.82 82.61 Blue
26 167.20 68.94 Blue
27 173.34 65.82 Green
28 167.01 76.51 Brown
29 170.23 79.24 Brown
30 178.74 77.71 Blue
31 163.43 61.81 Blue
32 180.31 94.09 Blue
33 168.53 69.69 Green
34 169.58 85.78 Brown
35 175.97 85.97 Brown
36 173.19 79.63 Grey
37 165.82 91.90 Brown
38 173.03 69.15 Grey
39 162.75 95.12 Green
40 164.45 93.99 Grey
41 175.54 77.45 Brown
42 166.70 77.73 Grey
43 158.98 79.52 Green
44 174.37 68.89 Grey
45 170.99 89.28 Green
46 167.66 84.95 Green
47 182.34 74.80 Brown
48 174.15 62.23 Grey
49 176.60 86.83 Grey
50 161.07 68.41 Brown
51 166.36 83.59 Grey
52 173.27 71.41 Green
53 175.49 68.40 Brown
54 167.13 79.32 Blue
55 172.50 82.05 Grey
56 165.99 74.08 Green
57 162.98 91.60 Grey
58 166.37 75.21 Grey
59 174.67 77.98 Blue
60 167.25 76.46 Brown
61 157.83 79.58 Green
62 172.01 79.38 Brown
63 180.78 81.01 Blue
64 175.35 84.88 Grey
65 175.62 74.80 Brown
66 164.61 79.68 Brown
67 170.32 81.83 Grey
68 160.59 87.83 Grey
69 171.89 90.22 Blue
70 172.00 85.25 Green
71 169.43 97.16 Brown
72 175.26 89.85 Green
73 175.91 56.43 Blue
74 165.28 85.46 Grey
75 167.97 89.26 Green
76 173.14 65.19 Grey
77 168.29 66.42 Brown
78 165.51 67.75 Brown
79 174.57 80.72 Grey
80 172.36 89.46 Green
81 169.43 74.64 Grey
82 164.26 86.70 Grey
83 168.24 94.37 Green
84 175.41 81.33 Brown
85 165.66 87.23 Brown
86 175.70 84.33 Grey
87 171.10 91.41 Green
88 157.42 92.50 Blue
89 172.88 93.83 Grey
90 170.68 70.06 Brown
91 163.25 72.35 Grey
92 181.34 97.84 Blue
93 171.33 73.41 Brown
94 176.86 70.74 Blue
95 173.33 61.56 Blue
96 169.36 80.01 Green
97 163.72 82.22 Grey
98 169.07 69.45 Brown
99 172.52 74.15 Grey
100 169.06 79.30 Brown
101 168.91 83.33 Brown
102 169.59 78.45 Blue
103 171.91 72.91 Grey
104 161.42 82.41 Grey
105 172.58 74.51 Brown
106 186.07 87.01 Blue
107 165.28 82.75 Green
108 182.94 78.19 Grey
109 172.87 83.34 Brown
110 168.60 93.30 Grey
111 162.79 81.64 Grey
112 177.03 87.75 Blue
113 167.12 80.36 Blue
114 175.06 84.90 Blue
115 158.82 95.08 Grey
116 171.76 89.64 Green
117 176.21 67.87 Green
118 165.87 91.06 Blue
119 163.02 71.34 Brown
120 160.85 77.43 Green
121 172.63 74.35 Grey
122 174.19 90.74 Blue
123 171.38 74.59 Blue
124 164.64 93.53 Brown
125 171.45 76.96 Brown
126 156.85 104.04 Blue
127 168.52 74.16 Brown
128 163.93 74.41 Brown
129 159.62 90.77 Green
130 170.10 81.71 Green
131 177.15 80.96 Grey
132 170.84 80.94 Green
133 167.33 68.45 Brown
134 170.27 77.24 Brown
135 172.25 89.71 Brown
136 171.89 66.62 Green
137 171.11 79.86 Brown
138 176.30 75.56 Green
139 164.53 56.66 Blue
140 162.85 78.12 Brown
141 170.68 93.57 Green
142 171.76 71.39 Brown
143 179.07 82.18 Grey
144 161.85 76.57 Brown
145 169.57 66.74 Blue
146 175.69 84.65 Brown
147 163.01 69.20 Brown
148 172.77 91.34 Grey
149 171.97 81.06 Brown
150 173.85 64.29 Blue
151 175.91 74.64 Blue
152 169.01 75.68 Blue
153 161.09 88.46 Grey
154 172.72 103.04 Grey
155 166.61 80.95 Green
156 172.72 79.53 Grey
157 164.56 76.90 Brown
158 174.67 67.85 Blue
159 176.40 69.11 Green
160 181.35 82.09 Blue
161 162.57 67.66 Green
162 164.55 66.22 Grey
163 174.47 68.13 Grey
164 164.30 68.03 Green
165 172.57 89.35 Green
166 174.83 79.28 Blue
167 184.49 70.14 Blue
168 168.56 94.75 Green
169 165.57 91.45 Brown
170 170.09 86.86 Green
171 158.88 75.32 Green
172 172.43 89.99 Green
173 165.65 88.76 Blue
174 169.14 91.15 Grey
175 163.46 75.12 Green
176 187.60 86.30 Brown
177 173.80 80.58 Blue
178 161.23 100.44 Brown
179 177.67 74.33 Grey
180 169.05 87.05 Grey
181 178.29 84.80 Blue
182 164.01 56.07 Green
183 165.98 88.18 Green
184 158.81 79.94 Green
185 165.00 79.08 Grey
186 181.59 73.98 Brown
187 178.51 97.71 Green
188 164.49 100.50 Grey
189 171.08 77.88 Brown
190 178.41 79.50 Grey
191 171.44 90.93 Grey
192 170.56 76.33 Brown
193 163.61 74.91 Brown
194 170.82 96.64 Blue
195 162.00 80.41 Blue
196 181.74 91.46 Grey
197 164.51 82.23 Brown
198 153.24 74.82 Green
199 170.33 86.33 Grey
200 168.13 80.89 Blue
201 175.68 88.07 Green
202 164.98 91.46 Brown
203 161.65 93.11 Brown
204 170.13 75.62 Green
205 171.49 74.96 Blue
206 155.08 69.49 Blue
207 175.33 74.79 Brown
208 162.10 69.98 Green
209 171.29 85.79 Brown
210 176.10 84.82 Grey
211 176.13 80.55 Green
212 178.30 82.79 Brown
213 164.93 79.95 Grey
214 163.46 82.00 Blue
215 168.70 93.44 Brown
216 177.62 74.46 Grey
217 173.39 81.92 Blue
218 167.89 78.19 Grey
219 178.44 74.67 Grey
220 156.72 82.71 Brown
221 161.40 65.70 Brown
222 178.23 94.59 Blue
223 174.12 88.85 Green
224 161.36 70.16 Brown
225 179.79 72.71 Brown
226 165.52 110.95 Blue
227 181.59 81.86 Grey
228 158.52 96.55 Grey
229 162.22 70.69 Brown
230 167.17 103.56 Brown
231 163.76 82.12 Green
232 162.00 71.40 Brown
233 180.66 86.27 Grey
234 173.24 78.15 Green
235 175.02 72.22 Grey
236 178.50 74.26 Brown
237 164.16 68.24 Grey
238 166.45 91.16 Grey
239 173.73 70.56 Blue
240 169.75 78.32 Grey
241 165.63 77.06 Grey
242 174.01 88.51 Blue
243 173.22 82.04 Blue
244 170.03 70.00 Brown
245 168.88 63.04 Brown
246 167.90 83.63 Green
247 170.32 75.21 Blue
248 171.18 83.83 Brown
249 177.71 53.75 Green
250 169.06 61.44 Blue
251 178.32 64.76 Brown
252 177.22 96.07 Grey
253 164.01 65.15 Brown
254 178.74 74.79 Green
255 161.24 83.80 Green
256 161.10 88.82 Brown
257 166.34 83.16 Grey
258 166.70 55.86 Green
259 175.33 76.17 Grey
260 175.64 84.98 Green
261 174.29 59.97 Brown
262 172.90 90.38 Blue
263 175.30 75.10 Blue
264 169.19 72.82 Grey
265 174.03 80.99 Blue
266 179.44 90.14 Grey
267 174.10 72.37 Grey
268 176.70 94.98 Green
269 173.52 83.62 Brown
270 156.02 102.49 Blue
271 171.92 86.97 Brown
272 173.33 76.52 Green
273 162.71 92.50 Blue
274 158.11 91.26 Brown
275 167.85 74.90 Grey
276 168.48 70.69 Blue
277 162.27 69.97 Grey
278 157.58 68.73 Blue
279 171.29 73.19 Blue
280 169.90 67.04 Green
281 164.64 80.08 Grey
282 162.18 70.32 Blue
283 167.27 75.40 Green
284 158.18 90.13 Grey
285 169.72 79.34 Blue
286 165.82 85.96 Green
287 173.74 75.47 Grey
288 167.84 74.05 Blue
289 171.83 63.39 Brown
290 173.12 71.08 Green
291 165.26 66.75 Grey
292 179.81 83.04 Blue
293 165.40 85.16 Brown
294 169.29 81.63 Brown
295 171.46 67.28 Blue
296 176.22 90.90 Green
297 152.23 62.18 Grey
298 183.04 80.21 Blue
299 173.79 100.41 Green
300 168.36 78.43 Grey
301 165.00 75.53 Grey
302 159.91 88.44 Brown
303 171.67 68.22 Blue
304 160.86 92.03 Blue
305 165.23 65.41 Grey
306 166.14 68.91 Brown
307 167.84 68.39 Green
308 177.34 76.93 Brown
309 174.78 75.44 Green
310 179.19 81.58 Grey
311 177.15 81.85 Brown
312 169.61 84.46 Grey
313 165.24 86.52 Brown
314 172.65 91.17 Grey
315 166.15 80.84 Blue
316 169.02 90.87 Blue
317 171.72 86.35 Blue
318 162.29 77.11 Grey
319 172.79 74.32 Brown
320 162.49 73.98 Grey
321 167.39 82.42 Green
322 175.02 80.40 Blue
323 171.05 94.77 Brown
324 187.02 83.80 Grey
325 173.32 79.28 Blue
326 159.82 82.18 Brown
327 174.22 72.66 Green
328 175.97 84.06 Brown
329 170.26 80.50 Blue
330 183.46 76.41 Brown
331 175.50 78.24 Grey
332 172.59 83.16 Green
333 174.16 88.49 Blue
334 161.19 76.21 Green
335 164.80 96.43 Green
336 167.49 78.51 Green
337 171.06 68.17 Blue
338 179.36 66.17 Brown
339 155.43 69.67 Blue
340 173.42 68.59 Blue
341 180.49 87.26 Green
342 175.88 77.59 Blue
343 168.87 85.74 Green
344 176.25 74.35 Brown
345 172.02 76.30 Blue
346 164.42 89.78 Green
347 174.24 78.44 Green
348 165.80 91.72 Grey
349 169.90 78.67 Green
350 162.92 86.79 Green
351 159.30 66.02 Grey
352 171.94 93.04 Blue
353 168.01 92.44 Grey
354 167.76 77.91 Green
355 177.17 75.44 Grey
356 175.38 82.54 Green
357 167.05 83.29 Green
358 172.70 67.65 Grey
359 175.30 89.98 Grey
360 173.76 83.69 Brown
361 171.04 70.76 Grey
362 173.68 88.58 Brown
363 163.37 85.51 Green
364 174.82 73.46 Brown
365 171.20 86.19 Brown
366 173.14 58.30 Brown
367 160.92 89.27 Blue
368 168.80 92.27 Grey
369 184.85 66.73 Blue
370 165.78 87.43 Green
371 178.97 74.01 Blue
372 170.45 91.30 Blue
373 175.79 91.01 Brown
374 184.39 95.42 Green
375 175.38 88.47 Blue
376 172.71 84.57 Brown
377 169.28 77.65 Green
378 165.51 86.93 Green
379 172.17 77.86 Green
380 177.42 87.14 Blue
381 170.19 74.74 Green
382 162.89 83.63 Brown
383 167.94 74.74 Green
384 162.26 93.41 Grey
385 167.82 89.49 Green
386 171.59 85.26 Brown
387 174.17 84.76 Brown
388 172.16 77.83 Blue
389 168.71 67.30 Brown
390 171.68 78.97 Grey
391 173.78 74.14 Blue
392 171.70 83.65 Blue
393 167.60 61.29 Brown
394 174.31 81.61 Green
395 165.28 62.35 Grey
396 171.30 88.05 Grey
397 178.16 79.32 Green
398 169.40 80.83 Grey
399 180.85 77.46 Grey
400 169.76 77.48 Brown
401 164.42 63.85 Green
402 157.76 83.73 Grey
403 171.46 84.19 Green
404 173.87 76.95 Blue
405 162.70 86.56 Blue
406 165.93 78.66 Grey
407 175.51 86.69 Brown
408 166.75 92.86 Green
409 168.84 89.72 Brown
410 170.88 85.31 Grey
411 179.91 63.75 Grey
412 155.69 72.33 Grey
413 171.75 68.22 Blue
414 172.60 102.21 Brown
415 180.15 89.35 Green
416 164.58 75.61 Green
417 169.16 69.59 Brown
418 164.75 72.48 Blue
419 181.88 92.77 Blue
420 173.12 75.30 Blue
421 183.04 71.73 Blue
422 182.25 92.94 Brown
423 162.75 86.24 Green
424 171.68 80.39 Grey
425 171.30 60.00 Green
426 175.96 78.88 Grey
427 171.26 84.36 Blue
428 175.44 87.89 Grey
429 161.88 88.80 Green
430 166.89 67.40 Brown
431 176.31 82.00 Blue
432 169.11 66.91 Blue
433 171.45 75.57 Blue
434 156.60 83.94 Grey
435 180.29 68.24 Grey
436 178.29 80.08 Green
437 173.24 71.46 Brown
438 164.42 84.45 Blue
439 169.35 79.27 Green
440 177.73 84.49 Brown
441 177.14 83.34 Brown
442 164.51 69.45 Green
443 161.76 90.05 Grey
444 170.78 65.54 Brown
445 168.60 82.71 Grey
446 167.15 61.88 Blue
447 171.45 82.18 Grey
448 181.69 77.38 Brown
449 168.16 74.63 Grey
450 174.33 81.86 Grey
451 175.31 81.44 Grey
452 166.74 75.98 Blue
453 166.11 81.80 Blue
454 168.42 89.50 Blue
455 179.78 84.53 Grey
456 172.87 72.82 Brown
457 160.19 80.82 Blue
458 173.20 73.75 Grey
459 157.64 67.81 Brown
460 174.05 53.40 Brown
461 166.16 82.55 Brown
462 167.73 86.96 Green
463 167.49 81.92 Green
464 167.29 74.25 Green
465 175.33 76.88 Blue
466 165.05 62.45 Green
467 168.60 62.08 Grey
468 177.32 95.72 Brown
469 171.95 86.58 Blue
470 168.62 74.65 Grey
471 176.16 77.12 Grey
472 160.46 70.83 Brown
473 164.83 86.24 Brown
474 174.98 56.24 Grey
475 168.42 79.30 Blue
476 164.34 76.26 Grey
477 171.81 85.73 Green
478 174.92 108.38 Grey
479 174.40 83.39 Green
480 164.13 71.42 Blue
481 175.85 80.53 Blue
482 154.94 79.10 Green
483 164.17 88.25 Blue
484 169.32 75.01 Green
485 172.98 92.08 Green
486 167.99 89.91 Green
487 167.85 77.09 Blue
488 165.75 67.04 Blue
489 174.59 62.18 Brown
490 159.21 87.10 Blue
491 169.29 62.57 Blue
492 178.47 71.07 Grey
493 171.67 79.73 Blue
494 176.90 81.48 Brown
495 175.93 72.86 Blue
496 178.44 64.71 Brown
497 159.35 69.50 Grey
498 165.33 82.78 Blue
499 167.99 81.33 Blue
500 171.35 75.67 Brown
501 166.09 73.93 Brown
502 179.17 89.79 Grey
503 164.92 86.12 Blue
504 170.11 82.76 Green
505 171.44 84.03 Green
506 170.41 73.62 Blue
507 164.98 70.22 Blue
508 176.53 88.59 Green
509 173.11 96.43 Blue
510 161.93 80.42 Blue
511 171.03 76.75 Brown
512 182.58 78.94 Blue
513 168.13 83.07 Blue
514 180.06 75.73 Blue
515 165.83 77.77 Brown
516 166.76 88.04 Blue
517 178.82 80.48 Blue
518 176.12 96.31 Brown
519 172.40 87.14 Brown
520 167.91 76.14 Brown
521 163.73 51.94 Grey
522 172.36 72.26 Green
523 163.94 67.49 Green
524 169.41 91.22 Blue
525 159.69 83.50 Green
526 163.72 96.98 Blue
527 175.74 76.92 Blue
528 167.61 84.33 Green
529 156.71 89.91 Grey
530 167.76 77.36 Green
531 158.38 75.30 Green
532 169.82 82.48 Blue
533 164.20 74.32 Blue
534 170.17 86.97 Blue
535 170.22 83.27 Blue
536 170.86 86.41 Green
537 175.19 82.90 Green
538 170.93 90.99 Green
539 165.79 79.10 Grey
540 172.38 79.26 Brown
541 163.69 68.79 Green
542 171.16 80.14 Blue
543 167.84 92.98 Brown
544 166.59 84.03 Grey
545 172.46 84.54 Brown
546 173.40 82.64 Grey
547 175.82 80.75 Green
548 162.82 80.26 Brown
549 170.88 80.20 Grey
550 177.71 91.28 Grey
551 162.69 75.73 Grey
552 162.38 93.35 Grey
553 170.24 68.03 Green
554 172.67 83.03 Green
555 166.09 79.73 Blue
556 167.25 91.16 Blue
557 169.11 90.34 Brown
558 169.01 69.28 Blue
559 167.85 71.41 Blue
560 165.06 77.27 Green
561 165.10 67.34 Grey
562 172.09 70.32 Blue
563 163.39 65.81 Grey
564 176.11 80.93 Grey
565 168.34 64.27 Brown
566 166.81 76.30 Brown
567 167.32 89.09 Grey
568 179.46 78.02 Brown
569 174.39 66.68 Brown
570 176.83 89.59 Grey
571 157.86 74.24 Green
572 171.68 74.10 Green
573 177.14 69.48 Grey
574 173.68 65.24 Grey
575 167.51 79.87 Green
576 175.48 83.14 Grey
577 180.23 79.88 Brown
578 172.81 79.77 Green
579 178.32 84.15 Brown
580 165.26 55.69 Green
581 173.60 79.77 Green
582 162.36 73.69 Brown
583 176.21 72.31 Green
584 175.49 103.02 Blue
585 165.12 87.70 Grey
586 173.57 88.38 Blue
587 176.04 85.30 Green
588 174.63 79.30 Green
589 158.76 73.01 Blue
590 161.63 90.70 Brown
591 168.38 72.95 Blue
592 173.18 81.45 Grey
593 167.22 63.72 Blue
594 176.40 79.11 Green
595 169.30 73.40 Grey
596 164.36 68.47 Brown
597 169.51 94.44 Brown
598 178.64 81.48 Grey
599 161.23 83.09 Brown
600 177.96 78.14 Green
601 167.29 76.52 Grey
602 155.73 68.38 Green
603 172.56 79.51 Green
604 172.43 81.79 Blue
605 177.12 71.10 Brown
606 188.40 77.76 Grey
607 163.86 77.96 Grey
608 179.89 81.58 Brown
609 171.55 81.18 Blue
610 160.59 67.18 Blue
611 170.71 75.65 Green
612 171.17 92.01 Blue
613 173.10 76.23 Brown
614 167.22 68.50 Green
615 168.76 84.82 Blue
616 181.38 80.17 Blue
617 169.01 89.39 Brown
618 177.44 84.38 Brown
619 169.28 73.88 Brown
620 168.02 88.87 Green
621 163.40 78.40 Grey
622 166.16 74.87 Brown
623 168.64 76.91 Blue
624 176.32 80.63 Brown
625 171.53 78.05 Grey
626 173.26 86.79 Green
627 175.98 78.86 Blue
628 176.61 81.64 Brown
629 172.46 78.30 Brown
630 173.27 88.45 Brown
631 171.14 83.32 Brown
632 173.53 72.04 Blue
633 177.32 82.48 Grey
634 167.17 76.51 Brown
635 166.77 78.16 Brown
636 172.41 91.55 Blue
637 172.25 99.12 Green
638 166.88 83.24 Blue
639 183.22 86.45 Blue
640 177.93 67.21 Brown
641 171.79 76.05 Brown
642 169.17 83.38 Grey
643 174.32 75.56 Blue
644 167.69 83.74 Blue
645 172.61 94.16 Brown
646 169.05 64.30 Brown
647 167.06 84.80 Blue
648 172.30 77.38 Blue
649 159.59 78.33 Grey
650 161.50 74.15 Green
651 162.46 74.35 Grey
652 170.06 71.58 Brown
653 162.63 71.55 Grey
654 165.84 80.89 Grey
655 177.79 95.91 Blue
656 180.93 83.49 Green
657 171.33 73.20 Grey
658 165.49 90.89 Grey
659 175.78 63.33 Blue
660 161.33 78.06 Blue
661 165.67 86.29 Grey
662 171.99 105.16 Grey
663 173.10 71.20 Blue
664 177.83 95.66 Grey
665 182.45 88.12 Grey
666 158.38 80.99 Grey
667 168.55 84.19 Brown
668 177.03 51.05 Blue
669 183.15 66.94 Green
670 164.35 84.65 Brown
671 172.21 79.38 Blue
672 164.96 82.63 Grey
673 170.71 92.57 Green
674 167.68 76.50 Brown
675 160.49 86.10 Blue
676 180.71 85.45 Blue
677 173.48 73.60 Grey
678 172.51 66.09 Grey
679 166.81 76.96 Grey
680 173.39 83.71 Blue
681 162.58 60.35 Grey
682 165.24 91.15 Grey
683 163.26 88.50 Grey
684 176.23 77.54 Blue
685 173.03 58.67 Green
686 163.21 79.55 Blue
687 172.63 108.89 Green
688 165.40 73.71 Brown
689 168.11 92.52 Green
690 182.90 83.68 Blue
691 183.16 89.71 Grey
692 163.06 59.48 Grey
693 169.33 90.72 Brown
694 160.87 75.61 Green
695 172.84 78.21 Brown
696 175.05 86.12 Blue
697 161.54 79.42 Grey
698 178.11 70.95 Green
699 171.46 77.15 Brown
700 167.06 80.20 Brown
701 166.14 69.30 Brown
702 171.00 89.52 Blue
703 169.81 67.83 Blue
704 159.79 72.46 Brown
705 177.15 93.35 Blue
706 174.64 85.09 Brown
707 166.32 62.53 Green
708 169.61 79.31 Brown
709 164.83 59.97 Brown
710 170.59 83.70 Grey
711 164.78 89.56 Blue
712 175.87 78.52 Grey
713 179.01 75.49 Green
714 173.05 92.14 Brown
715 172.60 80.50 Grey
716 173.12 82.11 Brown
717 169.43 92.11 Grey
718 169.72 86.67 Grey
719 161.56 77.44 Green
720 167.34 78.52 Green
721 162.20 94.25 Brown
722 166.67 85.44 Brown
723 173.51 74.21 Blue
724 163.76 83.11 Green
725 168.07 73.61 Blue
726 168.47 72.60 Brown
727 173.62 76.49 Grey
728 175.39 90.84 Green
729 163.72 67.37 Green
730 163.72 84.49 Grey
731 165.57 65.56 Blue
732 171.33 99.76 Grey
733 171.28 72.37 Green
734 168.45 73.16 Green
735 170.45 80.90 Blue
736 167.44 64.71 Blue
737 167.97 87.40 Green
738 163.68 71.95 Blue
739 167.22 73.07 Green
740 163.62 72.80 Brown
741 167.65 77.85 Brown
742 169.78 84.30 Brown
743 164.28 73.24 Grey
744 174.22 82.37 Blue
745 168.60 75.81 Grey
746 172.12 93.99 Brown
747 169.38 83.26 Blue
748 156.91 86.26 Blue
749 182.70 68.74 Green
750 172.36 79.18 Blue
751 173.62 73.62 Green
752 169.61 78.67 Blue
753 162.57 77.53 Grey
754 174.80 73.75 Green
755 170.38 80.12 Blue
756 169.82 68.36 Brown
757 169.64 85.50 Green
758 171.53 71.22 Green
759 171.88 75.61 Blue
760 167.53 75.49 Blue
761 170.05 85.28 Green
762 175.54 85.13 Grey
763 166.39 86.88 Blue
764 173.91 72.92 Grey
765 170.05 84.86 Grey
766 171.73 90.91 Green
767 159.17 77.30 Blue
768 171.27 70.99 Blue
769 165.70 70.39 Green
770 171.42 72.31 Brown
771 175.94 77.15 Blue
772 161.77 78.26 Green
773 164.25 70.37 Brown
774 177.28 84.03 Blue
775 171.03 62.43 Green
776 168.55 75.06 Green
777 169.97 68.97 Grey
778 175.41 101.88 Blue
779 172.35 75.31 Blue
780 164.17 52.74 Brown
781 162.42 91.86 Brown
782 171.13 88.97 Brown
783 168.85 86.50 Grey
784 169.01 80.83 Blue
785 178.82 77.34 Grey
786 168.43 70.15 Brown
787 169.97 76.14 Grey
788 165.86 82.54 Green
789 170.62 69.51 Blue
790 168.38 81.04 Grey
791 154.90 83.06 Blue
792 160.61 98.80 Blue
793 180.29 81.90 Grey
794 170.64 91.48 Grey
795 176.29 77.53 Blue
796 176.12 81.54 Blue
797 165.91 87.99 Green
798 165.93 77.68 Blue
799 178.16 85.93 Blue
800 175.77 85.49 Brown
801 168.94 81.48 Brown
802 171.87 72.87 Green
803 159.51 94.99 Green
804 165.89 71.66 Blue
805 163.28 75.08 Brown
806 171.00 81.93 Grey
807 181.44 75.80 Grey
808 177.86 86.79 Brown
809 164.56 73.89 Grey
810 162.51 73.49 Blue
811 173.79 62.71 Brown
812 171.37 76.59 Brown
813 165.31 80.23 Green
814 177.10 85.85 Brown
815 169.68 91.33 Blue
816 164.74 70.02 Blue
817 167.16 67.41 Grey
818 176.59 72.44 Green
819 167.67 87.14 Green
820 180.49 72.37 Grey
821 162.50 69.32 Brown
822 169.94 78.54 Green
823 187.97 70.20 Grey
824 167.72 69.66 Blue
825 168.77 71.80 Brown
826 161.77 82.84 Grey
827 169.82 65.56 Brown
828 166.66 91.34 Blue
829 158.60 84.16 Grey
830 168.39 87.68 Brown
831 165.63 85.80 Blue
832 176.14 100.40 Green
833 171.81 99.22 Green
834 175.88 86.69 Green
835 171.83 90.59 Green
836 171.45 70.71 Blue
837 173.18 77.73 Brown
838 162.56 86.50 Grey
839 174.99 80.90 Grey
840 164.13 65.63 Grey
841 171.43 79.27 Grey
842 164.59 84.02 Blue
843 180.31 85.98 Blue
844 164.68 85.91 Brown
845 178.58 77.20 Grey
846 167.26 94.25 Blue
847 174.98 87.42 Brown
848 171.12 80.85 Blue
849 172.87 89.16 Blue
850 161.29 52.25 Grey
851 163.68 80.18 Blue
852 165.10 79.56 Green
853 166.13 79.58 Blue
854 172.58 85.56 Green
855 170.28 72.88 Brown
856 164.84 79.77 Blue
857 164.69 85.92 Blue
858 167.08 88.43 Blue
859 172.56 89.59 Blue
860 182.45 89.65 Grey
861 165.60 70.04 Blue
862 168.40 81.91 Grey
863 171.27 81.36 Brown
864 179.48 58.56 Blue
865 165.98 65.24 Grey
866 175.08 86.60 Grey
867 174.34 93.30 Grey
868 179.48 81.04 Grey
869 175.10 83.07 Blue
870 164.93 88.78 Green
871 178.08 93.84 Brown
872 162.18 100.84 Grey
873 162.45 91.66 Green
874 178.52 74.95 Blue
875 170.70 70.36 Grey
876 157.12 79.51 Green
877 172.06 80.77 Brown
878 168.65 88.14 Grey
879 178.39 80.42 Brown
880 163.63 91.35 Brown
881 168.10 96.05 Green
882 180.39 79.33 Brown
883 166.21 82.65 Grey
884 170.57 69.78 Grey
885 165.62 85.22 Blue
886 163.20 60.96 Brown
887 158.47 93.38 Blue
888 172.20 87.47 Green
889 169.90 76.16 Brown
890 174.66 95.10 Green
891 170.76 93.98 Blue
892 169.07 81.23 Blue
893 170.46 73.18 Blue
894 167.13 73.57 Brown
895 167.90 87.90 Brown
896 178.66 82.78 Brown
897 163.04 76.75 Grey
898 165.78 90.71 Grey
899 164.24 76.56 Green
900 172.18 77.58 Green
901 174.40 76.92 Blue
902 166.06 86.66 Green
903 156.95 86.44 Brown
904 173.60 105.34 Blue
905 176.72 83.57 Grey
906 164.83 68.12 Blue
907 172.01 83.58 Grey
908 161.70 92.18 Grey
909 183.03 87.78 Brown
910 171.05 82.08 Green
911 170.72 90.51 Green
912 176.39 66.94 Blue
913 168.91 75.17 Blue
914 168.54 81.38 Grey
915 166.47 69.77 Brown
916 167.58 79.23 Brown
917 168.73 72.75 Green
918 180.46 74.60 Green
919 175.05 92.21 Blue
920 175.98 78.05 Grey
921 178.51 80.08 Blue
922 159.18 85.57 Grey
923 169.93 84.01 Grey
924 171.72 85.50 Blue
925 161.44 61.85 Green
926 165.99 72.48 Grey
927 173.22 74.47 Brown
928 171.24 73.69 Blue
929 169.16 94.97 Green
930 175.44 93.03 Grey
931 169.25 76.96 Blue
932 169.42 66.65 Green
933 171.58 89.62 Brown
934 159.75 99.11 Grey
935 170.92 70.30 Grey
936 163.26 83.64 Brown
937 164.49 88.78 Green
938 171.67 80.42 Blue
939 177.75 90.68 Grey
940 173.16 68.92 Blue
941 180.76 79.53 Brown
942 156.65 91.02 Grey
943 173.69 102.92 Green
944 176.76 91.69 Blue
945 170.00 93.39 Brown
946 173.21 64.55 Green
947 174.41 88.12 Grey
948 168.52 71.59 Blue
949 168.74 69.76 Blue
950 179.08 85.58 Grey
951 179.24 79.60 Green
952 172.49 89.09 Blue
953 161.18 80.76 Green
954 175.78 78.99 Green
955 171.44 106.49 Grey
956 170.57 63.71 Blue
957 167.48 70.57 Blue
958 186.46 75.52 Green
959 165.22 80.18 Grey
960 167.22 68.09 Green
961 169.37 86.47 Grey
962 174.09 81.82 Grey
963 168.94 84.84 Brown
964 162.93 74.48 Green
965 175.49 71.60 Blue
966 176.68 98.36 Blue
967 173.22 69.36 Green
968 169.15 88.18 Grey
969 163.27 65.43 Brown
970 177.11 92.81 Blue
971 168.72 77.29 Grey
972 167.28 87.93 Brown
973 175.06 84.13 Grey
974 167.44 91.47 Blue
975 174.41 94.54 Green
976 174.64 75.32 Blue
977 164.94 89.89 Grey
978 166.72 70.14 Grey
979 171.08 106.69 Grey
980 176.65 74.30 Green
981 159.56 77.14 Brown
982 168.35 59.00 Brown
983 167.41 78.85 Blue
984 164.90 91.11 Blue
985 178.38 68.21 Brown
986 166.34 69.16 Brown
987 166.38 72.98 Grey
988 172.06 96.09 Grey
989 177.11 78.19 Blue
990 168.11 71.96 Green
991 167.17 100.39 Green
992 168.57 68.26 Blue
993 166.45 102.61 Blue
994 178.34 87.51 Grey
995 184.94 67.57 Grey
996 177.16 76.20 Green
997 172.37 83.74 Brown
998 161.74 74.47 Green
999 165.14 81.01 Green
1000 167.96 85.23 Brown

Random assignment

I’m now going to flip (an imaginary, computer-generated) coin for each of these 1,000 individuals to assigned them to group A or B:

ID Height Weight Eye colour Group
1 164.29 72.48 Blue B
2 173.32 52.67 Brown A
3 164.59 91.12 Brown B
4 166.34 81.78 Grey B
5 166.41 83.85 Green B
6 178.75 81.98 Green A
7 169.14 71.24 Brown A
8 180.09 72.07 Grey A
9 173.46 68.81 Brown B
10 166.24 72.66 Brown A
11 177.61 79.56 Blue A
12 179.79 74.09 Brown B
13 174.14 89.51 Brown B
14 171.52 78.91 Green B
15 158.24 75.43 Green B
16 165.07 84.19 Grey A
17 180.27 92.09 Brown A
18 150.41 96.27 Brown A
19 180.02 71.62 Brown B
20 163.55 71.17 Blue A
21 175.05 82.77 Green A
22 171.54 98.17 Green A
23 159.25 79.06 Grey B
24 169.00 67.57 Brown B
25 170.82 82.61 Blue B
26 167.20 68.94 Blue B
27 173.34 65.82 Green B
28 167.01 76.51 Brown B
29 170.23 79.24 Brown A
30 178.74 77.71 Blue B
31 163.43 61.81 Blue A
32 180.31 94.09 Blue A
33 168.53 69.69 Green A
34 169.58 85.78 Brown B
35 175.97 85.97 Brown B
36 173.19 79.63 Grey A
37 165.82 91.90 Brown B
38 173.03 69.15 Grey B
39 162.75 95.12 Green B
40 164.45 93.99 Grey B
41 175.54 77.45 Brown A
42 166.70 77.73 Grey B
43 158.98 79.52 Green A
44 174.37 68.89 Grey A
45 170.99 89.28 Green B
46 167.66 84.95 Green B
47 182.34 74.80 Brown B
48 174.15 62.23 Grey A
49 176.60 86.83 Grey A
50 161.07 68.41 Brown A
51 166.36 83.59 Grey A
52 173.27 71.41 Green A
53 175.49 68.40 Brown B
54 167.13 79.32 Blue A
55 172.50 82.05 Grey A
56 165.99 74.08 Green A
57 162.98 91.60 Grey A
58 166.37 75.21 Grey A
59 174.67 77.98 Blue A
60 167.25 76.46 Brown B
61 157.83 79.58 Green A
62 172.01 79.38 Brown A
63 180.78 81.01 Blue B
64 175.35 84.88 Grey A
65 175.62 74.80 Brown A
66 164.61 79.68 Brown B
67 170.32 81.83 Grey B
68 160.59 87.83 Grey A
69 171.89 90.22 Blue A
70 172.00 85.25 Green A
71 169.43 97.16 Brown B
72 175.26 89.85 Green A
73 175.91 56.43 Blue A
74 165.28 85.46 Grey A
75 167.97 89.26 Green B
76 173.14 65.19 Grey A
77 168.29 66.42 Brown B
78 165.51 67.75 Brown A
79 174.57 80.72 Grey B
80 172.36 89.46 Green B
81 169.43 74.64 Grey A
82 164.26 86.70 Grey A
83 168.24 94.37 Green A
84 175.41 81.33 Brown A
85 165.66 87.23 Brown B
86 175.70 84.33 Grey A
87 171.10 91.41 Green A
88 157.42 92.50 Blue A
89 172.88 93.83 Grey A
90 170.68 70.06 Brown A
91 163.25 72.35 Grey A
92 181.34 97.84 Blue B
93 171.33 73.41 Brown B
94 176.86 70.74 Blue B
95 173.33 61.56 Blue B
96 169.36 80.01 Green A
97 163.72 82.22 Grey A
98 169.07 69.45 Brown B
99 172.52 74.15 Grey A
100 169.06 79.30 Brown B
101 168.91 83.33 Brown B
102 169.59 78.45 Blue B
103 171.91 72.91 Grey B
104 161.42 82.41 Grey A
105 172.58 74.51 Brown A
106 186.07 87.01 Blue B
107 165.28 82.75 Green B
108 182.94 78.19 Grey B
109 172.87 83.34 Brown B
110 168.60 93.30 Grey B
111 162.79 81.64 Grey B
112 177.03 87.75 Blue B
113 167.12 80.36 Blue A
114 175.06 84.90 Blue A
115 158.82 95.08 Grey A
116 171.76 89.64 Green B
117 176.21 67.87 Green B
118 165.87 91.06 Blue A
119 163.02 71.34 Brown A
120 160.85 77.43 Green B
121 172.63 74.35 Grey A
122 174.19 90.74 Blue B
123 171.38 74.59 Blue B
124 164.64 93.53 Brown A
125 171.45 76.96 Brown A
126 156.85 104.04 Blue A
127 168.52 74.16 Brown B
128 163.93 74.41 Brown B
129 159.62 90.77 Green B
130 170.10 81.71 Green B
131 177.15 80.96 Grey B
132 170.84 80.94 Green A
133 167.33 68.45 Brown A
134 170.27 77.24 Brown A
135 172.25 89.71 Brown B
136 171.89 66.62 Green B
137 171.11 79.86 Brown A
138 176.30 75.56 Green B
139 164.53 56.66 Blue B
140 162.85 78.12 Brown B
141 170.68 93.57 Green A
142 171.76 71.39 Brown A
143 179.07 82.18 Grey B
144 161.85 76.57 Brown B
145 169.57 66.74 Blue A
146 175.69 84.65 Brown A
147 163.01 69.20 Brown B
148 172.77 91.34 Grey B
149 171.97 81.06 Brown B
150 173.85 64.29 Blue A
151 175.91 74.64 Blue B
152 169.01 75.68 Blue B
153 161.09 88.46 Grey A
154 172.72 103.04 Grey A
155 166.61 80.95 Green A
156 172.72 79.53 Grey B
157 164.56 76.90 Brown B
158 174.67 67.85 Blue B
159 176.40 69.11 Green A
160 181.35 82.09 Blue B
161 162.57 67.66 Green B
162 164.55 66.22 Grey B
163 174.47 68.13 Grey B
164 164.30 68.03 Green A
165 172.57 89.35 Green A
166 174.83 79.28 Blue A
167 184.49 70.14 Blue A
168 168.56 94.75 Green B
169 165.57 91.45 Brown A
170 170.09 86.86 Green A
171 158.88 75.32 Green A
172 172.43 89.99 Green A
173 165.65 88.76 Blue A
174 169.14 91.15 Grey A
175 163.46 75.12 Green A
176 187.60 86.30 Brown A
177 173.80 80.58 Blue A
178 161.23 100.44 Brown B
179 177.67 74.33 Grey B
180 169.05 87.05 Grey B
181 178.29 84.80 Blue A
182 164.01 56.07 Green B
183 165.98 88.18 Green A
184 158.81 79.94 Green A
185 165.00 79.08 Grey A
186 181.59 73.98 Brown A
187 178.51 97.71 Green B
188 164.49 100.50 Grey A
189 171.08 77.88 Brown A
190 178.41 79.50 Grey A
191 171.44 90.93 Grey A
192 170.56 76.33 Brown B
193 163.61 74.91 Brown A
194 170.82 96.64 Blue B
195 162.00 80.41 Blue A
196 181.74 91.46 Grey B
197 164.51 82.23 Brown A
198 153.24 74.82 Green A
199 170.33 86.33 Grey A
200 168.13 80.89 Blue A
201 175.68 88.07 Green A
202 164.98 91.46 Brown B
203 161.65 93.11 Brown B
204 170.13 75.62 Green A
205 171.49 74.96 Blue B
206 155.08 69.49 Blue A
207 175.33 74.79 Brown A
208 162.10 69.98 Green B
209 171.29 85.79 Brown A
210 176.10 84.82 Grey B
211 176.13 80.55 Green B
212 178.30 82.79 Brown A
213 164.93 79.95 Grey A
214 163.46 82.00 Blue A
215 168.70 93.44 Brown A
216 177.62 74.46 Grey B
217 173.39 81.92 Blue B
218 167.89 78.19 Grey B
219 178.44 74.67 Grey B
220 156.72 82.71 Brown B
221 161.40 65.70 Brown A
222 178.23 94.59 Blue B
223 174.12 88.85 Green B
224 161.36 70.16 Brown B
225 179.79 72.71 Brown A
226 165.52 110.95 Blue A
227 181.59 81.86 Grey B
228 158.52 96.55 Grey B
229 162.22 70.69 Brown A
230 167.17 103.56 Brown A
231 163.76 82.12 Green B
232 162.00 71.40 Brown A
233 180.66 86.27 Grey A
234 173.24 78.15 Green B
235 175.02 72.22 Grey A
236 178.50 74.26 Brown A
237 164.16 68.24 Grey A
238 166.45 91.16 Grey B
239 173.73 70.56 Blue B
240 169.75 78.32 Grey B
241 165.63 77.06 Grey B
242 174.01 88.51 Blue A
243 173.22 82.04 Blue B
244 170.03 70.00 Brown B
245 168.88 63.04 Brown B
246 167.90 83.63 Green A
247 170.32 75.21 Blue B
248 171.18 83.83 Brown A
249 177.71 53.75 Green A
250 169.06 61.44 Blue B
251 178.32 64.76 Brown A
252 177.22 96.07 Grey A
253 164.01 65.15 Brown A
254 178.74 74.79 Green A
255 161.24 83.80 Green B
256 161.10 88.82 Brown B
257 166.34 83.16 Grey A
258 166.70 55.86 Green A
259 175.33 76.17 Grey B
260 175.64 84.98 Green B
261 174.29 59.97 Brown A
262 172.90 90.38 Blue B
263 175.30 75.10 Blue B
264 169.19 72.82 Grey B
265 174.03 80.99 Blue B
266 179.44 90.14 Grey A
267 174.10 72.37 Grey A
268 176.70 94.98 Green B
269 173.52 83.62 Brown B
270 156.02 102.49 Blue B
271 171.92 86.97 Brown A
272 173.33 76.52 Green A
273 162.71 92.50 Blue A
274 158.11 91.26 Brown A
275 167.85 74.90 Grey A
276 168.48 70.69 Blue A
277 162.27 69.97 Grey A
278 157.58 68.73 Blue B
279 171.29 73.19 Blue A
280 169.90 67.04 Green A
281 164.64 80.08 Grey A
282 162.18 70.32 Blue A
283 167.27 75.40 Green A
284 158.18 90.13 Grey A
285 169.72 79.34 Blue B
286 165.82 85.96 Green B
287 173.74 75.47 Grey A
288 167.84 74.05 Blue A
289 171.83 63.39 Brown B
290 173.12 71.08 Green B
291 165.26 66.75 Grey B
292 179.81 83.04 Blue B
293 165.40 85.16 Brown A
294 169.29 81.63 Brown B
295 171.46 67.28 Blue A
296 176.22 90.90 Green A
297 152.23 62.18 Grey A
298 183.04 80.21 Blue A
299 173.79 100.41 Green B
300 168.36 78.43 Grey B
301 165.00 75.53 Grey B
302 159.91 88.44 Brown B
303 171.67 68.22 Blue A
304 160.86 92.03 Blue B
305 165.23 65.41 Grey A
306 166.14 68.91 Brown B
307 167.84 68.39 Green A
308 177.34 76.93 Brown B
309 174.78 75.44 Green A
310 179.19 81.58 Grey B
311 177.15 81.85 Brown A
312 169.61 84.46 Grey A
313 165.24 86.52 Brown A
314 172.65 91.17 Grey A
315 166.15 80.84 Blue A
316 169.02 90.87 Blue A
317 171.72 86.35 Blue A
318 162.29 77.11 Grey A
319 172.79 74.32 Brown B
320 162.49 73.98 Grey B
321 167.39 82.42 Green A
322 175.02 80.40 Blue A
323 171.05 94.77 Brown B
324 187.02 83.80 Grey B
325 173.32 79.28 Blue B
326 159.82 82.18 Brown B
327 174.22 72.66 Green A
328 175.97 84.06 Brown A
329 170.26 80.50 Blue A
330 183.46 76.41 Brown A
331 175.50 78.24 Grey B
332 172.59 83.16 Green B
333 174.16 88.49 Blue B
334 161.19 76.21 Green B
335 164.80 96.43 Green B
336 167.49 78.51 Green A
337 171.06 68.17 Blue A
338 179.36 66.17 Brown A
339 155.43 69.67 Blue B
340 173.42 68.59 Blue B
341 180.49 87.26 Green A
342 175.88 77.59 Blue B
343 168.87 85.74 Green B
344 176.25 74.35 Brown B
345 172.02 76.30 Blue B
346 164.42 89.78 Green B
347 174.24 78.44 Green B
348 165.80 91.72 Grey B
349 169.90 78.67 Green B
350 162.92 86.79 Green A
351 159.30 66.02 Grey B
352 171.94 93.04 Blue B
353 168.01 92.44 Grey B
354 167.76 77.91 Green B
355 177.17 75.44 Grey A
356 175.38 82.54 Green A
357 167.05 83.29 Green A
358 172.70 67.65 Grey A
359 175.30 89.98 Grey B
360 173.76 83.69 Brown A
361 171.04 70.76 Grey A
362 173.68 88.58 Brown A
363 163.37 85.51 Green B
364 174.82 73.46 Brown A
365 171.20 86.19 Brown A
366 173.14 58.30 Brown A
367 160.92 89.27 Blue B
368 168.80 92.27 Grey B
369 184.85 66.73 Blue A
370 165.78 87.43 Green A
371 178.97 74.01 Blue A
372 170.45 91.30 Blue B
373 175.79 91.01 Brown A
374 184.39 95.42 Green A
375 175.38 88.47 Blue B
376 172.71 84.57 Brown B
377 169.28 77.65 Green A
378 165.51 86.93 Green A
379 172.17 77.86 Green B
380 177.42 87.14 Blue B
381 170.19 74.74 Green B
382 162.89 83.63 Brown A
383 167.94 74.74 Green B
384 162.26 93.41 Grey A
385 167.82 89.49 Green A
386 171.59 85.26 Brown A
387 174.17 84.76 Brown A
388 172.16 77.83 Blue A
389 168.71 67.30 Brown B
390 171.68 78.97 Grey A
391 173.78 74.14 Blue A
392 171.70 83.65 Blue A
393 167.60 61.29 Brown B
394 174.31 81.61 Green A
395 165.28 62.35 Grey A
396 171.30 88.05 Grey B
397 178.16 79.32 Green B
398 169.40 80.83 Grey B
399 180.85 77.46 Grey A
400 169.76 77.48 Brown A
401 164.42 63.85 Green B
402 157.76 83.73 Grey A
403 171.46 84.19 Green A
404 173.87 76.95 Blue B
405 162.70 86.56 Blue B
406 165.93 78.66 Grey A
407 175.51 86.69 Brown B
408 166.75 92.86 Green B
409 168.84 89.72 Brown B
410 170.88 85.31 Grey B
411 179.91 63.75 Grey B
412 155.69 72.33 Grey B
413 171.75 68.22 Blue B
414 172.60 102.21 Brown B
415 180.15 89.35 Green A
416 164.58 75.61 Green B
417 169.16 69.59 Brown B
418 164.75 72.48 Blue B
419 181.88 92.77 Blue A
420 173.12 75.30 Blue B
421 183.04 71.73 Blue A
422 182.25 92.94 Brown B
423 162.75 86.24 Green A
424 171.68 80.39 Grey B
425 171.30 60.00 Green B
426 175.96 78.88 Grey B
427 171.26 84.36 Blue A
428 175.44 87.89 Grey A
429 161.88 88.80 Green B
430 166.89 67.40 Brown B
431 176.31 82.00 Blue B
432 169.11 66.91 Blue B
433 171.45 75.57 Blue B
434 156.60 83.94 Grey B
435 180.29 68.24 Grey B
436 178.29 80.08 Green B
437 173.24 71.46 Brown B
438 164.42 84.45 Blue A
439 169.35 79.27 Green B
440 177.73 84.49 Brown B
441 177.14 83.34 Brown A
442 164.51 69.45 Green A
443 161.76 90.05 Grey A
444 170.78 65.54 Brown B
445 168.60 82.71 Grey A
446 167.15 61.88 Blue A
447 171.45 82.18 Grey B
448 181.69 77.38 Brown B
449 168.16 74.63 Grey A
450 174.33 81.86 Grey A
451 175.31 81.44 Grey A
452 166.74 75.98 Blue A
453 166.11 81.80 Blue A
454 168.42 89.50 Blue A
455 179.78 84.53 Grey B
456 172.87 72.82 Brown A
457 160.19 80.82 Blue B
458 173.20 73.75 Grey A
459 157.64 67.81 Brown B
460 174.05 53.40 Brown A
461 166.16 82.55 Brown B
462 167.73 86.96 Green B
463 167.49 81.92 Green A
464 167.29 74.25 Green A
465 175.33 76.88 Blue B
466 165.05 62.45 Green B
467 168.60 62.08 Grey A
468 177.32 95.72 Brown A
469 171.95 86.58 Blue B
470 168.62 74.65 Grey B
471 176.16 77.12 Grey A
472 160.46 70.83 Brown B
473 164.83 86.24 Brown A
474 174.98 56.24 Grey B
475 168.42 79.30 Blue A
476 164.34 76.26 Grey A
477 171.81 85.73 Green A
478 174.92 108.38 Grey B
479 174.40 83.39 Green A
480 164.13 71.42 Blue A
481 175.85 80.53 Blue A
482 154.94 79.10 Green A
483 164.17 88.25 Blue B
484 169.32 75.01 Green A
485 172.98 92.08 Green A
486 167.99 89.91 Green B
487 167.85 77.09 Blue A
488 165.75 67.04 Blue A
489 174.59 62.18 Brown B
490 159.21 87.10 Blue A
491 169.29 62.57 Blue A
492 178.47 71.07 Grey B
493 171.67 79.73 Blue B
494 176.90 81.48 Brown B
495 175.93 72.86 Blue B
496 178.44 64.71 Brown B
497 159.35 69.50 Grey B
498 165.33 82.78 Blue B
499 167.99 81.33 Blue B
500 171.35 75.67 Brown A
501 166.09 73.93 Brown B
502 179.17 89.79 Grey A
503 164.92 86.12 Blue B
504 170.11 82.76 Green A
505 171.44 84.03 Green B
506 170.41 73.62 Blue A
507 164.98 70.22 Blue A
508 176.53 88.59 Green B
509 173.11 96.43 Blue A
510 161.93 80.42 Blue A
511 171.03 76.75 Brown A
512 182.58 78.94 Blue A
513 168.13 83.07 Blue B
514 180.06 75.73 Blue B
515 165.83 77.77 Brown B
516 166.76 88.04 Blue A
517 178.82 80.48 Blue A
518 176.12 96.31 Brown B
519 172.40 87.14 Brown B
520 167.91 76.14 Brown A
521 163.73 51.94 Grey B
522 172.36 72.26 Green B
523 163.94 67.49 Green A
524 169.41 91.22 Blue B
525 159.69 83.50 Green B
526 163.72 96.98 Blue A
527 175.74 76.92 Blue B
528 167.61 84.33 Green B
529 156.71 89.91 Grey A
530 167.76 77.36 Green B
531 158.38 75.30 Green B
532 169.82 82.48 Blue B
533 164.20 74.32 Blue A
534 170.17 86.97 Blue A
535 170.22 83.27 Blue A
536 170.86 86.41 Green B
537 175.19 82.90 Green A
538 170.93 90.99 Green B
539 165.79 79.10 Grey A
540 172.38 79.26 Brown A
541 163.69 68.79 Green A
542 171.16 80.14 Blue A
543 167.84 92.98 Brown A
544 166.59 84.03 Grey A
545 172.46 84.54 Brown B
546 173.40 82.64 Grey B
547 175.82 80.75 Green B
548 162.82 80.26 Brown B
549 170.88 80.20 Grey A
550 177.71 91.28 Grey A
551 162.69 75.73 Grey A
552 162.38 93.35 Grey A
553 170.24 68.03 Green A
554 172.67 83.03 Green A
555 166.09 79.73 Blue B
556 167.25 91.16 Blue B
557 169.11 90.34 Brown A
558 169.01 69.28 Blue A
559 167.85 71.41 Blue A
560 165.06 77.27 Green A
561 165.10 67.34 Grey B
562 172.09 70.32 Blue A
563 163.39 65.81 Grey B
564 176.11 80.93 Grey A
565 168.34 64.27 Brown A
566 166.81 76.30 Brown B
567 167.32 89.09 Grey A
568 179.46 78.02 Brown A
569 174.39 66.68 Brown A
570 176.83 89.59 Grey A
571 157.86 74.24 Green A
572 171.68 74.10 Green A
573 177.14 69.48 Grey A
574 173.68 65.24 Grey A
575 167.51 79.87 Green A
576 175.48 83.14 Grey A
577 180.23 79.88 Brown B
578 172.81 79.77 Green B
579 178.32 84.15 Brown A
580 165.26 55.69 Green B
581 173.60 79.77 Green A
582 162.36 73.69 Brown A
583 176.21 72.31 Green A
584 175.49 103.02 Blue B
585 165.12 87.70 Grey A
586 173.57 88.38 Blue A
587 176.04 85.30 Green A
588 174.63 79.30 Green B
589 158.76 73.01 Blue A
590 161.63 90.70 Brown B
591 168.38 72.95 Blue A
592 173.18 81.45 Grey B
593 167.22 63.72 Blue A
594 176.40 79.11 Green B
595 169.30 73.40 Grey B
596 164.36 68.47 Brown A
597 169.51 94.44 Brown A
598 178.64 81.48 Grey A
599 161.23 83.09 Brown A
600 177.96 78.14 Green B
601 167.29 76.52 Grey B
602 155.73 68.38 Green B
603 172.56 79.51 Green A
604 172.43 81.79 Blue A
605 177.12 71.10 Brown A
606 188.40 77.76 Grey B
607 163.86 77.96 Grey B
608 179.89 81.58 Brown B
609 171.55 81.18 Blue B
610 160.59 67.18 Blue A
611 170.71 75.65 Green B
612 171.17 92.01 Blue A
613 173.10 76.23 Brown A
614 167.22 68.50 Green B
615 168.76 84.82 Blue B
616 181.38 80.17 Blue B
617 169.01 89.39 Brown B
618 177.44 84.38 Brown A
619 169.28 73.88 Brown B
620 168.02 88.87 Green B
621 163.40 78.40 Grey A
622 166.16 74.87 Brown B
623 168.64 76.91 Blue A
624 176.32 80.63 Brown A
625 171.53 78.05 Grey A
626 173.26 86.79 Green B
627 175.98 78.86 Blue B
628 176.61 81.64 Brown B
629 172.46 78.30 Brown A
630 173.27 88.45 Brown A
631 171.14 83.32 Brown A
632 173.53 72.04 Blue B
633 177.32 82.48 Grey B
634 167.17 76.51 Brown B
635 166.77 78.16 Brown B
636 172.41 91.55 Blue B
637 172.25 99.12 Green A
638 166.88 83.24 Blue B
639 183.22 86.45 Blue A
640 177.93 67.21 Brown B
641 171.79 76.05 Brown B
642 169.17 83.38 Grey A
643 174.32 75.56 Blue B
644 167.69 83.74 Blue B
645 172.61 94.16 Brown A
646 169.05 64.30 Brown A
647 167.06 84.80 Blue A
648 172.30 77.38 Blue A
649 159.59 78.33 Grey B
650 161.50 74.15 Green B
651 162.46 74.35 Grey A
652 170.06 71.58 Brown B
653 162.63 71.55 Grey A
654 165.84 80.89 Grey A
655 177.79 95.91 Blue B
656 180.93 83.49 Green A
657 171.33 73.20 Grey A
658 165.49 90.89 Grey B
659 175.78 63.33 Blue B
660 161.33 78.06 Blue B
661 165.67 86.29 Grey A
662 171.99 105.16 Grey A
663 173.10 71.20 Blue A
664 177.83 95.66 Grey B
665 182.45 88.12 Grey B
666 158.38 80.99 Grey B
667 168.55 84.19 Brown A
668 177.03 51.05 Blue A
669 183.15 66.94 Green A
670 164.35 84.65 Brown A
671 172.21 79.38 Blue A
672 164.96 82.63 Grey B
673 170.71 92.57 Green A
674 167.68 76.50 Brown A
675 160.49 86.10 Blue A
676 180.71 85.45 Blue B
677 173.48 73.60 Grey A
678 172.51 66.09 Grey B
679 166.81 76.96 Grey B
680 173.39 83.71 Blue B
681 162.58 60.35 Grey A
682 165.24 91.15 Grey A
683 163.26 88.50 Grey A
684 176.23 77.54 Blue A
685 173.03 58.67 Green B
686 163.21 79.55 Blue A
687 172.63 108.89 Green B
688 165.40 73.71 Brown A
689 168.11 92.52 Green B
690 182.90 83.68 Blue A
691 183.16 89.71 Grey B
692 163.06 59.48 Grey B
693 169.33 90.72 Brown A
694 160.87 75.61 Green B
695 172.84 78.21 Brown B
696 175.05 86.12 Blue A
697 161.54 79.42 Grey A
698 178.11 70.95 Green B
699 171.46 77.15 Brown B
700 167.06 80.20 Brown A
701 166.14 69.30 Brown A
702 171.00 89.52 Blue A
703 169.81 67.83 Blue B
704 159.79 72.46 Brown B
705 177.15 93.35 Blue A
706 174.64 85.09 Brown A
707 166.32 62.53 Green A
708 169.61 79.31 Brown B
709 164.83 59.97 Brown A
710 170.59 83.70 Grey B
711 164.78 89.56 Blue B
712 175.87 78.52 Grey A
713 179.01 75.49 Green A
714 173.05 92.14 Brown A
715 172.60 80.50 Grey B
716 173.12 82.11 Brown A
717 169.43 92.11 Grey B
718 169.72 86.67 Grey A
719 161.56 77.44 Green A
720 167.34 78.52 Green B
721 162.20 94.25 Brown B
722 166.67 85.44 Brown A
723 173.51 74.21 Blue A
724 163.76 83.11 Green B
725 168.07 73.61 Blue A
726 168.47 72.60 Brown B
727 173.62 76.49 Grey B
728 175.39 90.84 Green A
729 163.72 67.37 Green B
730 163.72 84.49 Grey B
731 165.57 65.56 Blue B
732 171.33 99.76 Grey B
733 171.28 72.37 Green B
734 168.45 73.16 Green A
735 170.45 80.90 Blue A
736 167.44 64.71 Blue B
737 167.97 87.40 Green B
738 163.68 71.95 Blue A
739 167.22 73.07 Green A
740 163.62 72.80 Brown B
741 167.65 77.85 Brown A
742 169.78 84.30 Brown A
743 164.28 73.24 Grey B
744 174.22 82.37 Blue B
745 168.60 75.81 Grey A
746 172.12 93.99 Brown B
747 169.38 83.26 Blue B
748 156.91 86.26 Blue B
749 182.70 68.74 Green B
750 172.36 79.18 Blue B
751 173.62 73.62 Green A
752 169.61 78.67 Blue A
753 162.57 77.53 Grey B
754 174.80 73.75 Green B
755 170.38 80.12 Blue A
756 169.82 68.36 Brown A
757 169.64 85.50 Green A
758 171.53 71.22 Green A
759 171.88 75.61 Blue B
760 167.53 75.49 Blue B
761 170.05 85.28 Green B
762 175.54 85.13 Grey A
763 166.39 86.88 Blue A
764 173.91 72.92 Grey A
765 170.05 84.86 Grey B
766 171.73 90.91 Green A
767 159.17 77.30 Blue B
768 171.27 70.99 Blue B
769 165.70 70.39 Green A
770 171.42 72.31 Brown B
771 175.94 77.15 Blue B
772 161.77 78.26 Green A
773 164.25 70.37 Brown B
774 177.28 84.03 Blue B
775 171.03 62.43 Green A
776 168.55 75.06 Green B
777 169.97 68.97 Grey B
778 175.41 101.88 Blue A
779 172.35 75.31 Blue A
780 164.17 52.74 Brown A
781 162.42 91.86 Brown B
782 171.13 88.97 Brown B
783 168.85 86.50 Grey B
784 169.01 80.83 Blue B
785 178.82 77.34 Grey A
786 168.43 70.15 Brown A
787 169.97 76.14 Grey B
788 165.86 82.54 Green B
789 170.62 69.51 Blue B
790 168.38 81.04 Grey B
791 154.90 83.06 Blue B
792 160.61 98.80 Blue A
793 180.29 81.90 Grey A
794 170.64 91.48 Grey A
795 176.29 77.53 Blue B
796 176.12 81.54 Blue A
797 165.91 87.99 Green B
798 165.93 77.68 Blue A
799 178.16 85.93 Blue B
800 175.77 85.49 Brown B
801 168.94 81.48 Brown B
802 171.87 72.87 Green B
803 159.51 94.99 Green A
804 165.89 71.66 Blue B
805 163.28 75.08 Brown A
806 171.00 81.93 Grey A
807 181.44 75.80 Grey B
808 177.86 86.79 Brown B
809 164.56 73.89 Grey B
810 162.51 73.49 Blue B
811 173.79 62.71 Brown A
812 171.37 76.59 Brown A
813 165.31 80.23 Green A
814 177.10 85.85 Brown A
815 169.68 91.33 Blue B
816 164.74 70.02 Blue A
817 167.16 67.41 Grey B
818 176.59 72.44 Green B
819 167.67 87.14 Green A
820 180.49 72.37 Grey B
821 162.50 69.32 Brown B
822 169.94 78.54 Green A
823 187.97 70.20 Grey B
824 167.72 69.66 Blue B
825 168.77 71.80 Brown A
826 161.77 82.84 Grey A
827 169.82 65.56 Brown A
828 166.66 91.34 Blue B
829 158.60 84.16 Grey A
830 168.39 87.68 Brown A
831 165.63 85.80 Blue B
832 176.14 100.40 Green A
833 171.81 99.22 Green B
834 175.88 86.69 Green A
835 171.83 90.59 Green A
836 171.45 70.71 Blue B
837 173.18 77.73 Brown A
838 162.56 86.50 Grey B
839 174.99 80.90 Grey B
840 164.13 65.63 Grey A
841 171.43 79.27 Grey A
842 164.59 84.02 Blue B
843 180.31 85.98 Blue A
844 164.68 85.91 Brown B
845 178.58 77.20 Grey A
846 167.26 94.25 Blue B
847 174.98 87.42 Brown B
848 171.12 80.85 Blue B
849 172.87 89.16 Blue B
850 161.29 52.25 Grey B
851 163.68 80.18 Blue B
852 165.10 79.56 Green B
853 166.13 79.58 Blue B
854 172.58 85.56 Green B
855 170.28 72.88 Brown A
856 164.84 79.77 Blue A
857 164.69 85.92 Blue A
858 167.08 88.43 Blue B
859 172.56 89.59 Blue A
860 182.45 89.65 Grey B
861 165.60 70.04 Blue A
862 168.40 81.91 Grey A
863 171.27 81.36 Brown A
864 179.48 58.56 Blue B
865 165.98 65.24 Grey A
866 175.08 86.60 Grey A
867 174.34 93.30 Grey A
868 179.48 81.04 Grey A
869 175.10 83.07 Blue A
870 164.93 88.78 Green B
871 178.08 93.84 Brown A
872 162.18 100.84 Grey A
873 162.45 91.66 Green A
874 178.52 74.95 Blue A
875 170.70 70.36 Grey A
876 157.12 79.51 Green A
877 172.06 80.77 Brown B
878 168.65 88.14 Grey A
879 178.39 80.42 Brown B
880 163.63 91.35 Brown A
881 168.10 96.05 Green A
882 180.39 79.33 Brown A
883 166.21 82.65 Grey B
884 170.57 69.78 Grey A
885 165.62 85.22 Blue B
886 163.20 60.96 Brown B
887 158.47 93.38 Blue A
888 172.20 87.47 Green A
889 169.90 76.16 Brown B
890 174.66 95.10 Green B
891 170.76 93.98 Blue B
892 169.07 81.23 Blue A
893 170.46 73.18 Blue B
894 167.13 73.57 Brown A
895 167.90 87.90 Brown A
896 178.66 82.78 Brown B
897 163.04 76.75 Grey A
898 165.78 90.71 Grey A
899 164.24 76.56 Green B
900 172.18 77.58 Green B
901 174.40 76.92 Blue A
902 166.06 86.66 Green A
903 156.95 86.44 Brown B
904 173.60 105.34 Blue A
905 176.72 83.57 Grey A
906 164.83 68.12 Blue A
907 172.01 83.58 Grey A
908 161.70 92.18 Grey A
909 183.03 87.78 Brown B
910 171.05 82.08 Green B
911 170.72 90.51 Green B
912 176.39 66.94 Blue A
913 168.91 75.17 Blue B
914 168.54 81.38 Grey B
915 166.47 69.77 Brown A
916 167.58 79.23 Brown A
917 168.73 72.75 Green A
918 180.46 74.60 Green B
919 175.05 92.21 Blue A
920 175.98 78.05 Grey B
921 178.51 80.08 Blue B
922 159.18 85.57 Grey A
923 169.93 84.01 Grey B
924 171.72 85.50 Blue B
925 161.44 61.85 Green A
926 165.99 72.48 Grey B
927 173.22 74.47 Brown B
928 171.24 73.69 Blue A
929 169.16 94.97 Green A
930 175.44 93.03 Grey A
931 169.25 76.96 Blue B
932 169.42 66.65 Green A
933 171.58 89.62 Brown A
934 159.75 99.11 Grey B
935 170.92 70.30 Grey A
936 163.26 83.64 Brown B
937 164.49 88.78 Green A
938 171.67 80.42 Blue B
939 177.75 90.68 Grey B
940 173.16 68.92 Blue B
941 180.76 79.53 Brown A
942 156.65 91.02 Grey A
943 173.69 102.92 Green A
944 176.76 91.69 Blue B
945 170.00 93.39 Brown B
946 173.21 64.55 Green A
947 174.41 88.12 Grey A
948 168.52 71.59 Blue B
949 168.74 69.76 Blue B
950 179.08 85.58 Grey B
951 179.24 79.60 Green A
952 172.49 89.09 Blue A
953 161.18 80.76 Green B
954 175.78 78.99 Green A
955 171.44 106.49 Grey A
956 170.57 63.71 Blue B
957 167.48 70.57 Blue A
958 186.46 75.52 Green B
959 165.22 80.18 Grey B
960 167.22 68.09 Green B
961 169.37 86.47 Grey B
962 174.09 81.82 Grey B
963 168.94 84.84 Brown A
964 162.93 74.48 Green A
965 175.49 71.60 Blue B
966 176.68 98.36 Blue B
967 173.22 69.36 Green B
968 169.15 88.18 Grey A
969 163.27 65.43 Brown B
970 177.11 92.81 Blue A
971 168.72 77.29 Grey A
972 167.28 87.93 Brown A
973 175.06 84.13 Grey B
974 167.44 91.47 Blue A
975 174.41 94.54 Green B
976 174.64 75.32 Blue B
977 164.94 89.89 Grey B
978 166.72 70.14 Grey B
979 171.08 106.69 Grey A
980 176.65 74.30 Green B
981 159.56 77.14 Brown A
982 168.35 59.00 Brown B
983 167.41 78.85 Blue B
984 164.90 91.11 Blue A
985 178.38 68.21 Brown B
986 166.34 69.16 Brown A
987 166.38 72.98 Grey B
988 172.06 96.09 Grey A
989 177.11 78.19 Blue A
990 168.11 71.96 Green B
991 167.17 100.39 Green A
992 168.57 68.26 Blue B
993 166.45 102.61 Blue A
994 178.34 87.51 Grey B
995 184.94 67.57 Grey B
996 177.16 76.20 Green B
997 172.37 83.74 Brown A
998 161.74 74.47 Green A
999 165.14 81.01 Green B
1000 167.96 85.23 Brown B

How similar are these groups?

Let’s first check their heights:

How similar are these groups?

And their weights:

How similar are these groups?

And their eye colors:

Making sure this wasn’t a fluke

Let’s re-run this:

ID Height Weight Eye colour Group
1 164.29 72.48 Blue A
2 173.32 52.67 Brown B
3 164.59 91.12 Brown A
4 166.34 81.78 Grey A
5 166.41 83.85 Green A
6 178.75 81.98 Green A
7 169.14 71.24 Brown A
8 180.09 72.07 Grey A
9 173.46 68.81 Brown B
10 166.24 72.66 Brown A
11 177.61 79.56 Blue B
12 179.79 74.09 Brown B
13 174.14 89.51 Brown A
14 171.52 78.91 Green A
15 158.24 75.43 Green B
16 165.07 84.19 Grey B
17 180.27 92.09 Brown A
18 150.41 96.27 Brown A
19 180.02 71.62 Brown B
20 163.55 71.17 Blue A
21 175.05 82.77 Green A
22 171.54 98.17 Green A
23 159.25 79.06 Grey A
24 169.00 67.57 Brown A
25 170.82 82.61 Blue B
26 167.20 68.94 Blue A
27 173.34 65.82 Green A
28 167.01 76.51 Brown B
29 170.23 79.24 Brown A
30 178.74 77.71 Blue B
31 163.43 61.81 Blue A
32 180.31 94.09 Blue B
33 168.53 69.69 Green B
34 169.58 85.78 Brown B
35 175.97 85.97 Brown B
36 173.19 79.63 Grey B
37 165.82 91.90 Brown B
38 173.03 69.15 Grey B
39 162.75 95.12 Green A
40 164.45 93.99 Grey B
41 175.54 77.45 Brown B
42 166.70 77.73 Grey A
43 158.98 79.52 Green A
44 174.37 68.89 Grey B
45 170.99 89.28 Green A
46 167.66 84.95 Green A
47 182.34 74.80 Brown B
48 174.15 62.23 Grey B
49 176.60 86.83 Grey B
50 161.07 68.41 Brown B
51 166.36 83.59 Grey B
52 173.27 71.41 Green A
53 175.49 68.40 Brown A
54 167.13 79.32 Blue A
55 172.50 82.05 Grey A
56 165.99 74.08 Green A
57 162.98 91.60 Grey B
58 166.37 75.21 Grey A
59 174.67 77.98 Blue A
60 167.25 76.46 Brown B
61 157.83 79.58 Green A
62 172.01 79.38 Brown B
63 180.78 81.01 Blue B
64 175.35 84.88 Grey B
65 175.62 74.80 Brown B
66 164.61 79.68 Brown A
67 170.32 81.83 Grey B
68 160.59 87.83 Grey B
69 171.89 90.22 Blue B
70 172.00 85.25 Green A
71 169.43 97.16 Brown A
72 175.26 89.85 Green A
73 175.91 56.43 Blue B
74 165.28 85.46 Grey B
75 167.97 89.26 Green A
76 173.14 65.19 Grey A
77 168.29 66.42 Brown A
78 165.51 67.75 Brown A
79 174.57 80.72 Grey B
80 172.36 89.46 Green A
81 169.43 74.64 Grey A
82 164.26 86.70 Grey B
83 168.24 94.37 Green A
84 175.41 81.33 Brown B
85 165.66 87.23 Brown B
86 175.70 84.33 Grey A
87 171.10 91.41 Green B
88 157.42 92.50 Blue B
89 172.88 93.83 Grey B
90 170.68 70.06 Brown B
91 163.25 72.35 Grey B
92 181.34 97.84 Blue A
93 171.33 73.41 Brown B
94 176.86 70.74 Blue A
95 173.33 61.56 Blue A
96 169.36 80.01 Green A
97 163.72 82.22 Grey A
98 169.07 69.45 Brown A
99 172.52 74.15 Grey B
100 169.06 79.30 Brown B
101 168.91 83.33 Brown A
102 169.59 78.45 Blue A
103 171.91 72.91 Grey A
104 161.42 82.41 Grey B
105 172.58 74.51 Brown A
106 186.07 87.01 Blue B
107 165.28 82.75 Green B
108 182.94 78.19 Grey A
109 172.87 83.34 Brown A
110 168.60 93.30 Grey B
111 162.79 81.64 Grey B
112 177.03 87.75 Blue A
113 167.12 80.36 Blue B
114 175.06 84.90 Blue B
115 158.82 95.08 Grey A
116 171.76 89.64 Green B
117 176.21 67.87 Green B
118 165.87 91.06 Blue A
119 163.02 71.34 Brown B
120 160.85 77.43 Green A
121 172.63 74.35 Grey A
122 174.19 90.74 Blue A
123 171.38 74.59 Blue A
124 164.64 93.53 Brown A
125 171.45 76.96 Brown A
126 156.85 104.04 Blue A
127 168.52 74.16 Brown B
128 163.93 74.41 Brown B
129 159.62 90.77 Green B
130 170.10 81.71 Green A
131 177.15 80.96 Grey B
132 170.84 80.94 Green B
133 167.33 68.45 Brown A
134 170.27 77.24 Brown A
135 172.25 89.71 Brown A
136 171.89 66.62 Green A
137 171.11 79.86 Brown A
138 176.30 75.56 Green B
139 164.53 56.66 Blue A
140 162.85 78.12 Brown B
141 170.68 93.57 Green A
142 171.76 71.39 Brown A
143 179.07 82.18 Grey B
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512 182.58 78.94 Blue A
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515 165.83 77.77 Brown B
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584 175.49 103.02 Blue A
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645 172.61 94.16 Brown B
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660 161.33 78.06 Blue A
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663 173.10 71.20 Blue B
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665 182.45 88.12 Grey B
666 158.38 80.99 Grey B
667 168.55 84.19 Brown A
668 177.03 51.05 Blue A
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684 176.23 77.54 Blue B
685 173.03 58.67 Green B
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721 162.20 94.25 Brown A
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723 173.51 74.21 Blue B
724 163.76 83.11 Green B
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731 165.57 65.56 Blue A
732 171.33 99.76 Grey A
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748 156.91 86.26 Blue B
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786 168.43 70.15 Brown A
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788 165.86 82.54 Green A
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790 168.38 81.04 Grey A
791 154.90 83.06 Blue A
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794 170.64 91.48 Grey A
795 176.29 77.53 Blue A
796 176.12 81.54 Blue A
797 165.91 87.99 Green A
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799 178.16 85.93 Blue A
800 175.77 85.49 Brown B
801 168.94 81.48 Brown B
802 171.87 72.87 Green A
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805 163.28 75.08 Brown B
806 171.00 81.93 Grey A
807 181.44 75.80 Grey A
808 177.86 86.79 Brown A
809 164.56 73.89 Grey A
810 162.51 73.49 Blue B
811 173.79 62.71 Brown A
812 171.37 76.59 Brown A
813 165.31 80.23 Green A
814 177.10 85.85 Brown A
815 169.68 91.33 Blue B
816 164.74 70.02 Blue A
817 167.16 67.41 Grey A
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819 167.67 87.14 Green B
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821 162.50 69.32 Brown B
822 169.94 78.54 Green B
823 187.97 70.20 Grey B
824 167.72 69.66 Blue B
825 168.77 71.80 Brown A
826 161.77 82.84 Grey A
827 169.82 65.56 Brown A
828 166.66 91.34 Blue B
829 158.60 84.16 Grey B
830 168.39 87.68 Brown B
831 165.63 85.80 Blue A
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833 171.81 99.22 Green B
834 175.88 86.69 Green B
835 171.83 90.59 Green B
836 171.45 70.71 Blue A
837 173.18 77.73 Brown B
838 162.56 86.50 Grey B
839 174.99 80.90 Grey A
840 164.13 65.63 Grey A
841 171.43 79.27 Grey B
842 164.59 84.02 Blue B
843 180.31 85.98 Blue A
844 164.68 85.91 Brown A
845 178.58 77.20 Grey B
846 167.26 94.25 Blue A
847 174.98 87.42 Brown A
848 171.12 80.85 Blue A
849 172.87 89.16 Blue A
850 161.29 52.25 Grey B
851 163.68 80.18 Blue A
852 165.10 79.56 Green A
853 166.13 79.58 Blue A
854 172.58 85.56 Green B
855 170.28 72.88 Brown A
856 164.84 79.77 Blue B
857 164.69 85.92 Blue A
858 167.08 88.43 Blue A
859 172.56 89.59 Blue A
860 182.45 89.65 Grey B
861 165.60 70.04 Blue B
862 168.40 81.91 Grey B
863 171.27 81.36 Brown A
864 179.48 58.56 Blue A
865 165.98 65.24 Grey A
866 175.08 86.60 Grey B
867 174.34 93.30 Grey A
868 179.48 81.04 Grey A
869 175.10 83.07 Blue B
870 164.93 88.78 Green B
871 178.08 93.84 Brown B
872 162.18 100.84 Grey B
873 162.45 91.66 Green B
874 178.52 74.95 Blue A
875 170.70 70.36 Grey A
876 157.12 79.51 Green A
877 172.06 80.77 Brown A
878 168.65 88.14 Grey B
879 178.39 80.42 Brown B
880 163.63 91.35 Brown B
881 168.10 96.05 Green B
882 180.39 79.33 Brown A
883 166.21 82.65 Grey B
884 170.57 69.78 Grey B
885 165.62 85.22 Blue A
886 163.20 60.96 Brown B
887 158.47 93.38 Blue B
888 172.20 87.47 Green A
889 169.90 76.16 Brown B
890 174.66 95.10 Green A
891 170.76 93.98 Blue B
892 169.07 81.23 Blue A
893 170.46 73.18 Blue A
894 167.13 73.57 Brown B
895 167.90 87.90 Brown A
896 178.66 82.78 Brown A
897 163.04 76.75 Grey A
898 165.78 90.71 Grey B
899 164.24 76.56 Green B
900 172.18 77.58 Green B
901 174.40 76.92 Blue B
902 166.06 86.66 Green A
903 156.95 86.44 Brown A
904 173.60 105.34 Blue B
905 176.72 83.57 Grey A
906 164.83 68.12 Blue B
907 172.01 83.58 Grey B
908 161.70 92.18 Grey B
909 183.03 87.78 Brown A
910 171.05 82.08 Green B
911 170.72 90.51 Green A
912 176.39 66.94 Blue A
913 168.91 75.17 Blue B
914 168.54 81.38 Grey B
915 166.47 69.77 Brown B
916 167.58 79.23 Brown B
917 168.73 72.75 Green B
918 180.46 74.60 Green A
919 175.05 92.21 Blue A
920 175.98 78.05 Grey A
921 178.51 80.08 Blue A
922 159.18 85.57 Grey A
923 169.93 84.01 Grey A
924 171.72 85.50 Blue B
925 161.44 61.85 Green A
926 165.99 72.48 Grey A
927 173.22 74.47 Brown A
928 171.24 73.69 Blue A
929 169.16 94.97 Green A
930 175.44 93.03 Grey A
931 169.25 76.96 Blue B
932 169.42 66.65 Green B
933 171.58 89.62 Brown A
934 159.75 99.11 Grey B
935 170.92 70.30 Grey A
936 163.26 83.64 Brown A
937 164.49 88.78 Green B
938 171.67 80.42 Blue A
939 177.75 90.68 Grey B
940 173.16 68.92 Blue B
941 180.76 79.53 Brown B
942 156.65 91.02 Grey B
943 173.69 102.92 Green B
944 176.76 91.69 Blue A
945 170.00 93.39 Brown B
946 173.21 64.55 Green B
947 174.41 88.12 Grey B
948 168.52 71.59 Blue A
949 168.74 69.76 Blue A
950 179.08 85.58 Grey B
951 179.24 79.60 Green A
952 172.49 89.09 Blue A
953 161.18 80.76 Green B
954 175.78 78.99 Green A
955 171.44 106.49 Grey A
956 170.57 63.71 Blue B
957 167.48 70.57 Blue B
958 186.46 75.52 Green A
959 165.22 80.18 Grey A
960 167.22 68.09 Green A
961 169.37 86.47 Grey B
962 174.09 81.82 Grey B
963 168.94 84.84 Brown B
964 162.93 74.48 Green A
965 175.49 71.60 Blue B
966 176.68 98.36 Blue A
967 173.22 69.36 Green B
968 169.15 88.18 Grey B
969 163.27 65.43 Brown B
970 177.11 92.81 Blue B
971 168.72 77.29 Grey B
972 167.28 87.93 Brown B
973 175.06 84.13 Grey B
974 167.44 91.47 Blue B
975 174.41 94.54 Green B
976 174.64 75.32 Blue B
977 164.94 89.89 Grey A
978 166.72 70.14 Grey A
979 171.08 106.69 Grey A
980 176.65 74.30 Green B
981 159.56 77.14 Brown B
982 168.35 59.00 Brown A
983 167.41 78.85 Blue A
984 164.90 91.11 Blue A
985 178.38 68.21 Brown B
986 166.34 69.16 Brown B
987 166.38 72.98 Grey A
988 172.06 96.09 Grey B
989 177.11 78.19 Blue A
990 168.11 71.96 Green B
991 167.17 100.39 Green B
992 168.57 68.26 Blue B
993 166.45 102.61 Blue A
994 178.34 87.51 Grey B
995 184.94 67.57 Grey B
996 177.16 76.20 Green B
997 172.37 83.74 Brown B
998 161.74 74.47 Green B
999 165.14 81.01 Green B
1000 167.96 85.23 Brown B

Check how similar they are

Increasingly similar

In fact, if we did this many, many, many times, these groups would be, on average, increasingly identical!

Why?

  • Central limit theorem

  • Law of large numbers

Do international monitors deter election-day fraud?

Yes!

  • The international community monitored the 2003 Armenian Presidential elections
  • Monitors were assigned randomly to the polling stations
  • Hyde found a big average difference between the vote share received by the cheating party at monitored stations compared to non-monitored stations.